We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (upper frame bound) for the difference between the two GSI systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI system to preserve the frame property.

中文翻译：

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广义平移不变系统的截断

我们提供了广义平移不变（GSI）系统可以通过生成器在傅立叶域中具有紧凑支持的 GSI 系统来近似的条件。近似质量将根据两个 GSI 系统之间差异的贝塞尔界（上框架界）来测量。特别是，这导致了 GSI 系统扰动的易于验证的条件，以保留框架属性。